Any idea how to find at least one "n" such that:
[ ( x^{1/n} + y^{1/n} ) / 2 ]^{2n }- xy < epsilon
2 <= x <= a, 2 <= y <= a
for any epsilon?
Actually, its well-known that:
lim [ ( x^{1/n} + y^{1/n} ) / 2 ]^{2n = xy}
Any idea how to find at least one "n" such that:
[ ( x^{1/n} + y^{1/n} ) / 2 ]^{2n }- xy < epsilon
2 <= x <= a, 2 <= y <= a
for any epsilon?
Actually, its well-known that:
lim [ ( x^{1/n} + y^{1/n} ) / 2 ]^{2n = xy}